Arc shift number and Region arc shift number for virtual knots

Amrendra Gill; Kirandeep Kaur; Prabhakar Madeti

doi:10.4134/JKMS.j180615

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2019; 56(4): 1063-1081

Online first article April 9, 2019 Printed July 1, 2019

https://doi.org/10.4134/JKMS.j180615

Arc shift number and Region arc shift number for virtual knots

Amrendra Gill, Kirandeep Kaur, Prabhakar Madeti

Indian Institute of Technology Ropar; Indian Institute of Technology Ropar; Indian Institute of Technology Ropar

Abstract

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Abstract

In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtual knot diagram can be turned into trivial knot using arc shift (region arc shift) moves. Based upon the arc shift move and region arc shift move, we define two virtual knot invariants, arc shift number and region arc shift number respectively.

Keywords: virtual knot, Gauss diagram, forbidden moves

MSC numbers: 57M25, 57M27